@article{14849, abstract = {We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J and Xu, Yuanyuan}, issn = {0091-1798}, journal = {The Annals of Probability}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability}, number = {6}, pages = {2192--2242}, publisher = {Institute of Mathematical Statistics}, title = {{On the rightmost eigenvalue of non-Hermitian random matrices}}, doi = {10.1214/23-aop1643}, volume = {51}, year = {2023}, } @article{14499, abstract = {An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables. The proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.}, author = {Kwan, Matthew Alan and Sah, Ashwin and Sauermann, Lisa and Sawhney, Mehtaab}, issn = {2050-5086}, journal = {Forum of Mathematics, Pi}, keywords = {Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Analysis}, publisher = {Cambridge University Press}, title = {{Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture}}, doi = {10.1017/fmp.2023.17}, volume = {11}, year = {2023}, } @article{14750, abstract = {Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution of the limiting ESDs of A and B, denoted as μα  μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions have a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math. Phys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. }, author = {Ding, Xiucai and Ji, Hong Chang}, issn = {1050-5164}, journal = {The Annals of Applied Probability}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability}, number = {4}, pages = {2981--3009}, publisher = {Institute of Mathematical Statistics}, title = {{Local laws for multiplication of random matrices}}, doi = {10.1214/22-aap1882}, volume = {33}, year = {2023}, } @article{14775, abstract = {We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble.}, author = {Schnelli, Kevin and Xu, Yuanyuan}, issn = {1050-5164}, journal = {The Annals of Applied Probability}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability}, number = {1}, pages = {677--725}, publisher = {Institute of Mathematical Statistics}, title = {{Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices}}, doi = {10.1214/22-aap1826}, volume = {33}, year = {2023}, } @article{14780, abstract = {In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.}, author = {Ding, Xiucai and Ji, Hong Chang}, issn = {1879-209X}, journal = {Stochastic Processes and their Applications}, keywords = {Applied Mathematics, Modeling and Simulation, Statistics and Probability}, pages = {25--60}, publisher = {Elsevier}, title = {{Spiked multiplicative random matrices and principal components}}, doi = {10.1016/j.spa.2023.05.009}, volume = {163}, year = {2023}, } @article{12178, abstract = {In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.}, author = {Agresti, Antonio and Hieber, Matthias and Hussein, Amru and Saal, Martin}, issn = {2194-041X}, journal = {Stochastics and Partial Differential Equations: Analysis and Computations}, keywords = {Applied Mathematics, Modeling and Simulation, Statistics and Probability}, publisher = {Springer Nature}, title = {{The stochastic primitive equations with transport noise and turbulent pressure}}, doi = {10.1007/s40072-022-00277-3}, year = {2022}, } @article{12281, abstract = {We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle.}, author = {Franceschini, Chiara and Gonçalves, Patrícia and Sau, Federico}, issn = {1350-7265}, journal = {Bernoulli}, keywords = {Statistics and Probability}, number = {2}, pages = {1340--1381}, publisher = {Bernoulli Society for Mathematical Statistics and Probability}, title = {{Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics}}, doi = {10.3150/21-bej1390}, volume = {28}, year = {2022}, } @article{12290, abstract = {We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {1083-6489}, journal = {Electronic Journal of Probability}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability}, pages = {1--38}, publisher = {Institute of Mathematical Statistics}, title = {{Optimal multi-resolvent local laws for Wigner matrices}}, doi = {10.1214/22-ejp838}, volume = {27}, year = {2022}, } @article{12480, abstract = {We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the performance of AMP in the high-dimensional limit can be succinctly characterized under suitable model assumptions; AMP can also be tailored to the empirical distribution of the signal entries, and for a wide class of estimation problems, AMP is conjectured to be optimal among all polynomial-time algorithms. However, a major issue of AMP is that in many models (such as phase retrieval), it requires an initialization correlated with the ground-truth signal and independent from the measurement matrix. Assuming that such an initialization is available is typically not realistic. In this paper, we solve this problem by proposing an AMP algorithm initialized with a spectral estimator. With such an initialization, the standard AMP analysis fails since the spectral estimator depends in a complicated way on the design matrix. Our main contribution is a rigorous characterization of the performance of AMP with spectral initialization in the high-dimensional limit. The key technical idea is to define and analyze a two-phase artificial AMP algorithm that first produces the spectral estimator, and then closely approximates the iterates of the true AMP. We also provide numerical results that demonstrate the validity of the proposed approach.}, author = {Mondelli, Marco and Venkataramanan, Ramji}, issn = {1742-5468}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability, Statistical and Nonlinear Physics}, number = {11}, publisher = {IOP Publishing}, title = {{Approximate message passing with spectral initialization for generalized linear models}}, doi = {10.1088/1742-5468/ac9828}, volume = {2022}, year = {2022}, } @article{10643, abstract = {We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap. }, author = {Henheik, Sven Joscha and Teufel, Stefan}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, keywords = {computational mathematics, discrete mathematics and combinatorics, geometry and topology, mathematical physics, statistics and probability, algebra and number theory, theoretical computer science, analysis}, publisher = {Cambridge University Press}, title = {{Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk}}, doi = {10.1017/fms.2021.80}, volume = {10}, year = {2022}, } @article{11135, abstract = {We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.}, author = {Reker, Jana}, issn = {2010-3271}, journal = {Random Matrices: Theory and Applications}, keywords = {Discrete Mathematics and Combinatorics, Statistics, Probability and Uncertainty, Statistics and Probability, Algebra and Number Theory}, number = {4}, publisher = {World Scientific}, title = {{On the operator norm of a Hermitian random matrix with correlated entries}}, doi = {10.1142/s2010326322500368}, volume = {11}, year = {2022}, } @article{12148, abstract = {We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.}, author = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J}, issn = {2050-5094}, journal = {Forum of Mathematics, Sigma}, keywords = {Computational Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, Algebra and Number Theory, Theoretical Computer Science, Analysis}, publisher = {Cambridge University Press}, title = {{Rank-uniform local law for Wigner matrices}}, doi = {10.1017/fms.2022.86}, volume = {10}, year = {2022}, } @article{9158, abstract = {While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.}, author = {De Nicola, Stefano}, issn = {1742-5468}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability, Statistical and Nonlinear Physics}, number = {1}, publisher = {IOP Publishing}, title = {{Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation}}, doi = {10.1088/1742-5468/abc7c7}, volume = {2021}, year = {2021}, } @article{9387, abstract = {We report the complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This result suggests that fixation of a deleterious allele that follows a click of the Muller’s ratchet is governed by natural selection, instead of random drift.}, author = {Khudiakova, Kseniia and Neretina, Tatiana Yu. and Kondrashov, Alexey S.}, issn = {0022-5193}, journal = {Journal of Theoretical Biology}, keywords = {General Biochemistry, Genetics and Molecular Biology, Modelling and Simulation, Statistics and Probability, General Immunology and Microbiology, Applied Mathematics, General Agricultural and Biological Sciences, General Medicine}, publisher = {Elsevier }, title = {{Two linked loci under mutation-selection balance and Muller’s ratchet}}, doi = {10.1016/j.jtbi.2021.110729}, volume = {524}, year = {2021}, } @article{14125, abstract = {Motivation: Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed. Results: We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively.}, author = {Stark, Stefan G and Ficek, Joanna and Locatello, Francesco and Bonilla, Ximena and Chevrier, Stéphane and Singer, Franziska and Aebersold, Rudolf and Al-Quaddoomi, Faisal S and Albinus, Jonas and Alborelli, Ilaria and Andani, Sonali and Attinger, Per-Olof and Bacac, Marina and Baumhoer, Daniel and Beck-Schimmer, Beatrice and Beerenwinkel, Niko and Beisel, Christian and Bernasconi, Lara and Bertolini, Anne and Bodenmiller, Bernd and Bonilla, Ximena and Casanova, Ruben and Chevrier, Stéphane and Chicherova, Natalia and D'Costa, Maya and Danenberg, Esther and Davidson, Natalie and gan, Monica-Andreea Dră and Dummer, Reinhard and Engler, Stefanie and Erkens, Martin and Eschbach, Katja and Esposito, Cinzia and Fedier, André and Ferreira, Pedro and Ficek, Joanna and Frei, Anja L and Frey, Bruno and Goetze, Sandra and Grob, Linda and Gut, Gabriele and Günther, Detlef and Haberecker, Martina and Haeuptle, Pirmin and Heinzelmann-Schwarz, Viola and Herter, Sylvia and Holtackers, Rene and Huesser, Tamara and Irmisch, Anja and Jacob, Francis and Jacobs, Andrea and Jaeger, Tim M and Jahn, Katharina and James, Alva R and Jermann, Philip M and Kahles, André and Kahraman, Abdullah and Koelzer, Viktor H and Kuebler, Werner and Kuipers, Jack and Kunze, Christian P and Kurzeder, Christian and Lehmann, Kjong-Van and Levesque, Mitchell and Lugert, Sebastian and Maass, Gerd and Manz, Markus and Markolin, Philipp and Mena, Julien and Menzel, Ulrike and Metzler, Julian M and Miglino, Nicola and Milani, Emanuela S and Moch, Holger and Muenst, Simone and Murri, Riccardo and Ng, Charlotte KY and Nicolet, Stefan and Nowak, Marta and Pedrioli, Patrick GA and Pelkmans, Lucas and Piscuoglio, Salvatore and Prummer, Michael and Ritter, Mathilde and Rommel, Christian and Rosano-González, María L and Rätsch, Gunnar and Santacroce, Natascha and Castillo, Jacobo Sarabia del and Schlenker, Ramona and Schwalie, Petra C and Schwan, Severin and Schär, Tobias and Senti, Gabriela and Singer, Franziska and Sivapatham, Sujana and Snijder, Berend and Sobottka, Bettina and Sreedharan, Vipin T and Stark, Stefan and Stekhoven, Daniel J and Theocharides, Alexandre PA and Thomas, Tinu M and Tolnay, Markus and Tosevski, Vinko and Toussaint, Nora C and Tuncel, Mustafa A and Tusup, Marina and Drogen, Audrey Van and Vetter, Marcus and Vlajnic, Tatjana and Weber, Sandra and Weber, Walter P and Wegmann, Rebekka and Weller, Michael and Wendt, Fabian and Wey, Norbert and Wicki, Andreas and Wollscheid, Bernd and Yu, Shuqing and Ziegler, Johanna and Zimmermann, Marc and Zoche, Martin and Zuend, Gregor and Rätsch, Gunnar and Lehmann, Kjong-Van}, issn = {1367-4811}, journal = {Bioinformatics}, keywords = {Computational Mathematics, Computational Theory and Mathematics, Computer Science Applications, Molecular Biology, Biochemistry, Statistics and Probability}, number = {Supplement_2}, pages = {i919--i927}, publisher = {Oxford University Press}, title = {{SCIM: Universal single-cell matching with unpaired feature sets}}, doi = {10.1093/bioinformatics/btaa843}, volume = {36}, year = {2020}, } @article{11507, abstract = {Lyman-α (Lyα) is intrinsically the brightest line emitted from active galaxies. While it originates from many physical processes, for star-forming galaxies the intrinsic Lyα luminosity is a direct tracer of the Lyman-continuum (LyC) radiation produced by the most massive O- and early-type B-stars (M⋆ ≳ 10 M⊙) with lifetimes of a few Myrs. As such, Lyα luminosity should be an excellent instantaneous star formation rate (SFR) indicator. However, its resonant nature and susceptibility to dust as a rest-frame UV photon makes Lyα very hard to interpret due to the uncertain Lyα escape fraction, fesc, Lyα. Here we explore results from the CAlibrating LYMan-α with Hα (CALYMHA) survey at z = 2.2, follow-up of Lyα emitters (LAEs) at z = 2.2 − 2.6 and a z ∼ 0−0.3 compilation of LAEs to directly measure fesc, Lyα with Hα. We derive a simple empirical relation that robustly retrieves fesc, Lyα as a function of Lyα rest-frame EW (EW0): fesc,Lyα = 0.0048 EW0[Å] ± 0.05 and we show that it constrains a well-defined anti-correlation between ionisation efficiency (ξion) and dust extinction in LAEs. Observed Lyα luminosities and EW0 are easy measurable quantities at high redshift, thus making our relation a practical tool to estimate intrinsic Lyα and LyC luminosities under well controlled and simple assumptions. Our results allow observed Lyα luminosities to be used to compute SFRs for LAEs at z ∼ 0−2.6 within ±0.2 dex of the Hα dust corrected SFRs. We apply our empirical SFR(Lyα,EW0) calibration to several sources at z ≥ 2.6 to find that star-forming LAEs have SFRs typically ranging from 0.1 to 20 M⊙ yr−1 and that our calibration might be even applicable for the most luminous LAEs within the epoch of re-ionisation. Our results imply high ionisation efficiencies (log10[ξion/Hz erg−1] = 25.4−25.6) and low dust content in LAEs across cosmic time, and will be easily tested with future observations with JWST which can obtain Hα and Hβ measurements for high-redshift LAEs.}, author = {Sobral, David and Matthee, Jorryt J}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, galaxies: high-redshift / galaxies: star formation / galaxies: statistics / galaxies: evolution / galaxies: formation / galaxies: ISM}, publisher = {EDP Sciences}, title = {{Predicting Lyα escape fractions with a simple observable: Lyα in emission as an empirically calibrated star formation rate indicator}}, doi = {10.1051/0004-6361/201833075}, volume = {623}, year = {2019}, } @article{11615, abstract = {The recently published Kepler mission Data Release 25 (DR25) reported on ∼197 000 targets observed during the mission. Despite this, no wide search for red giants showing solar-like oscillations have been made across all stars observed in Kepler’s long-cadence mode. In this work, we perform this task using custom apertures on the Kepler pixel files and detect oscillations in 21 914 stars, representing the largest sample of solar-like oscillating stars to date. We measure their frequency at maximum power, νmax, down to νmax≃4μHz and obtain log (g) estimates with a typical uncertainty below 0.05 dex, which is superior to typical measurements from spectroscopy. Additionally, the νmax distribution of our detections show good agreement with results from a simulated model of the Milky Way, with a ratio of observed to predicted stars of 0.992 for stars with 10<νmax<270μHz. Among our red giant detections, we find 909 to be dwarf/subgiant stars whose flux signal is polluted by a neighbouring giant as a result of using larger photometric apertures than those used by the NASA Kepler science processing pipeline. We further find that only 293 of the polluting giants are known Kepler targets. The remainder comprises over 600 newly identified oscillating red giants, with many expected to belong to the Galactic halo, serendipitously falling within the Kepler pixel files of targeted stars.}, author = {Hon, Marc and Stello, Dennis and García, Rafael A and Mathur, Savita and Sharma, Sanjib and Colman, Isabel L and Bugnet, Lisa Annabelle}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, asteroseismology, methods: data analysis, techniques: image processing, stars: oscillations, stars: statistics}, number = {4}, pages = {5616--5630}, publisher = {Oxford University Press}, title = {{A search for red giant solar-like oscillations in all Kepler data}}, doi = {10.1093/mnras/stz622}, volume = {485}, year = {2019}, } @article{8421, abstract = {The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends and completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards into complex domains (with respect to the angle), and to thoroughly analyze the nature of their complex singularities. As an application, we are able to prove some spectral rigidity results for elliptic domains.}, author = {Kaloshin, Vadim and Sorrentino, Alfonso}, issn = {0003-486X}, journal = {Annals of Mathematics}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability}, number = {1}, pages = {315--380}, publisher = {Annals of Mathematics, Princeton U}, title = {{On the local Birkhoff conjecture for convex billiards}}, doi = {10.4007/annals.2018.188.1.6}, volume = {188}, year = {2018}, } @article{11558, abstract = {We present and explore deep narrow- and medium-band data obtained with the Subaru and the Isaac Newton Telescopes in the ∼2 deg2 COSMOS field. We use these data as an extremely wide, low-resolution (R ∼ 20–80) Integral Field Unit survey to slice through the COSMOS field and obtain a large sample of ∼4000 Ly α emitters (LAEs) from z ∼ 2 to 6 in 16 redshift slices (SC4K). We present new Ly α luminosity functions (LFs) covering a comoving volume of ∼108 Mpc3. SC4K extensively complements ultradeep surveys, jointly covering over 4 dex in Ly α luminosity and revealing a global (2.5 < z < 6) synergy LF with α=−1.93+0.12−0.12⁠, log10Φ∗Lyα=−3.45+0.22−0.29 Mpc−3, and log10L∗Lyα=42.93+0.15−0.11 erg s−1. The Schechter component of the Ly α LF reveals a factor ∼5 rise in L∗Lyα and a ∼7 × decline in Φ∗Lyα from z ∼ 2 to 6. The data reveal an extra power-law (or Schechter) component above LLy α ≈ 1043.3 erg s−1 at z ∼ 2.2–3.5 and we show that it is partially driven by X-ray and radio active galactic nucleus (AGN), as their Ly α LF resembles the excess. The power-law component vanishes and/or is below our detection limits above z > 3.5, likely linked with the evolution of the AGN population. The Ly α luminosity density rises by a factor ∼2 from z ∼ 2 to 3 but is then found to be roughly constant (⁠1.1+0.2−0.2×1040 erg s−1 Mpc−3) to z ∼ 6, despite the ∼0.7 dex drop in ultraviolet (UV) luminosity density. The Ly α/UV luminosity density ratio rises from 4 ± 1 per cent to 30 ± 6 per cent from z ∼ 2.2 to 6. Our results imply a rise of a factor of ≈2 in the global ionization efficiency (ξion) and a factor ≈4 ± 1 in the Ly α escape fraction from z ∼ 2 to 6, hinting for evolution in both the typical burstiness/stellar populations and even more so in the typical interstellar medium conditions allowing Ly α photons to escape.}, author = {Sobral, David and Santos, Sérgio and Matthee, Jorryt J and Paulino-Afonso, Ana and Ribeiro, Bruno and Calhau, João and Khostovan, Ali A}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, galaxies: evolution, galaxies: formation, galaxies: high-redshift, galaxies: luminosity function, mass function, galaxies: statistics}, number = {4}, pages = {4725--4752}, publisher = {Oxford University Press}, title = {{Slicing COSMOS with SC4K: The evolution of typical Ly α emitters and the Ly α escape fraction from z ∼ 2 to 6}}, doi = {10.1093/mnras/sty378}, volume = {476}, year = {2018}, } @article{11562, abstract = {We present the CAlibrating LYMan-α with Hα (CALYMHA) pilot survey and new results on Lyman α (Lyα) selected galaxies at z ∼ 2. We use a custom-built Lyα narrow-band filter at the Isaac Newton Telescope, designed to provide a matched volume coverage to the z = 2.23 Hα HiZELS survey. Here, we present the first results for the COSMOS and UDS fields. Our survey currently reaches a 3σ line flux limit of ∼4 × 10−17 erg s−1 cm−2, and a Lyα luminosity limit of ∼1042.3 erg s−1. We find 188 Lyα emitters over 7.3 × 105 Mpc3, but also find significant numbers of other line-emitting sources corresponding to He II, C III] and C IV emission lines. These sources are important contaminants, and we carefully remove them, unlike most previous studies. We find that the Lyα luminosity function at z = 2.23 is very well described by a Schechter function up to LLy α ≈ 1043 erg s−1 with L∗=1042.59+0.16−0.08 erg s−1, ϕ∗=10−3.09+0.14−0.34 Mpc−3 and α = −1.75 ± 0.25. Above LLy α ≈ 1043 erg s−1, the Lyα luminosity function becomes power-law like, driven by X-ray AGN. We find that Lyα-selected emitters have a high escape fraction of 37 ± 7 per cent, anticorrelated with Lyα luminosity and correlated with Lyα equivalent width. Lyα emitters have ubiquitous large (≈40 kpc) Lyα haloes, ∼2 times larger than their Hα extents. By directly comparing our Lyα and Hα luminosity functions, we find that the global/overall escape fraction of Lyα photons (within a 13 kpc radius) from the full population of star-forming galaxies is 5.1 ± 0.2 per cent at the peak of the star formation history. An extra 3.3 ± 0.3 per cent of Lyα photons likely still escape, but at larger radii.}, author = {Sobral, David and Matthee, Jorryt J and Best, Philip and Stroe, Andra and Röttgering, Huub and Oteo, Iván and Smail, Ian and Morabito, Leah and Paulino-Afonso, Ana}, issn = {1365-2966}, journal = {Monthly Notices of the Royal Astronomical Society}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, galaxies: evolution, galaxies: haloes, galaxies: high-redshift, galaxies: luminosity function, mass function, galaxies: statistics, cosmology: observations}, number = {1}, pages = {1242--1258}, publisher = {Oxford University Press}, title = {{The CALYMHA survey: Lyα luminosity function and global escape fraction of Lyα photons at z = 2.23}}, doi = {10.1093/mnras/stw3090}, volume = {466}, year = {2017}, }